SesiĆ³n 3
Ana Escoto
23/10/2021
Previo
Volvamos a la base de la EHPM.
use "datos/ehpm_2019", clear
gladder money if actpr2012==10 & money>0
Relaciones grƔficas
TransformaciĆ³n logaritmica
gen log_money=log(money) if actpr2012==10
(47,267 missing values generated)Para hacer grĆ”ficos de dos variables, se usa ātwowayā, no dice que cada eje es una variable.
Veamos cĆ³mo se ve un grĆ”fico de este tipo:
twoway scatter log_money aproba1 if actpr2012==10 & money>0
La opciĆ³n ājitterā nos puede ayudar ver mejor quĆ© sucede y tambiĆ©n bajĆ”ndole la intensidad al color
twoway scatter money aproba1 if actpr2012==10 & money>0, jitter(50) mcolor(%20)
Estos grĆ”ficos nos permiten ver la relaciĆ³n positiva que existe, no entre los ingresos por hora, si no de los logaritmos de los ingresos por hora frente a los aƱos aprobados de escolaridad.
Estos grĆ”ficos quizĆ”s nos proveen informaciĆ³n a nosotros pero son dĆficiles de comunicar
Otra forma para ver la relaciĆ³n y su acelaracĆ³n
graph bar (mean) money if actpr2012==10, over(aproba1)
graph box money if actpr2012==10, over(aproba1)
Ojo con la representatividad
Modelo de regresiĆ³n lineal simple
Podemos describir una relaciĆ³n Para la poblaciĆ³n, como hemos observado, tenemos que usar letras griegas y tambiĆ©n incluir un elemento de error para nuestras estimaciones, De ahĆ que las anteriores ecuaciones se escriben tĆ©rminos poblacionales de la siguiente forma:
\[y=\beta_o+\beta_1x +\epsilon\]
Donde los parĆ”metros \(\beta_o\) y \(\beta_1\) describen la pendiente y el intercepto de la poblaciĆ³n, respectivamente.
Si quisiĆ©ramos ver cĆ³mo se ve esta lĆnea para nuestro ejemplo:
twoway lfit log_money aproba1 if actpr2012==10
Claramente aquĆ no vemos los datos. Podemos verlos:
twoway (scatter log_money aproba1 if actpr2012==10 , jitter(50) mcolor(%20)) ///
(lfit log_money aproba1 if actpr2012==10 )
> (lfit log_money aproba1 if actpr2012==10 )
ĀæCĆ³mo se ajusta esta lĆnea?
regress log_money aproba1 if actpr2012==10 Source | SS df MS Number of obs = 27,181
-------------+---------------------------------- F(1, 27179) = 5486.65
Model | 2625.67642 1 2625.67642 Prob > F = 0.0000
Residual | 13006.7148 27,179 .47855752 R-squared = 0.1680
-------------+---------------------------------- Adj R-squared = 0.1679
Total | 15632.3913 27,180 .575143166 Root MSE = .69178
------------------------------------------------------------------------------
log_money | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
aproba1 | .0641594 .0008662 74.07 0.000 .0624616 .0658571
_cons | 4.972621 .0082022 606.25 0.000 4.956544 4.988698
------------------------------------------------------------------------------Podemos poner entonces esa estimaciĆ³n un margen de confianza:
twoway (scatter log_money aproba1 if actpr2012==10 , jitter(50) mcolor(%20)) ///
(lfitci log_money aproba1 if actpr2012==10 )
> (lfitci log_money aproba1 if actpr2012==10 )
Vamos a instalar dos paquetes
ssc install estout, replace
ssc install coefplot, replacecoefplot
esttab (1)
log_money
----------------------------
aproba1 0.0642***
(74.07)
_cons 4.973***
(606.25)
----------------------------
N 27181
----------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001Para estos comando y para tener mƔs clara nuestras estimaciones habrƔ que guardar nuestors resultados:
estimates store modelo0 // guarda el Ćŗltimo modelo que se ha corrido
estimates replay // corre el Ćŗltimo modelo corrido
estimates replay modelo0 // corre el modelo0 independientemente si ha corrido otro
Model modelo0
-------------------------------------------------------------------------------------------------------------
Source | SS df MS Number of obs = 27,181
-------------+---------------------------------- F(1, 27179) = 5486.65
Model | 2625.67642 1 2625.67642 Prob > F = 0.0000
Residual | 13006.7148 27,179 .47855752 R-squared = 0.1680
-------------+---------------------------------- Adj R-squared = 0.1679
Total | 15632.3913 27,180 .575143166 Root MSE = .69178
------------------------------------------------------------------------------
log_money | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
aproba1 | .0641594 .0008662 74.07 0.000 .0624616 .0658571
_cons | 4.972621 .0082022 606.25 0.000 4.956544 4.988698
------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------
Model modelo0
-------------------------------------------------------------------------------------------------------------
Source | SS df MS Number of obs = 27,181
-------------+---------------------------------- F(1, 27179) = 5486.65
Model | 2625.67642 1 2625.67642 Prob > F = 0.0000
Residual | 13006.7148 27,179 .47855752 R-squared = 0.1680
-------------+---------------------------------- Adj R-squared = 0.1679
Total | 15632.3913 27,180 .575143166 Root MSE = .69178
------------------------------------------------------------------------------
log_money | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
aproba1 | .0641594 .0008662 74.07 0.000 .0624616 .0658571
_cons | 4.972621 .0082022 606.25 0.000 4.956544 4.988698
------------------------------------------------------------------------------
svyset correlativo [pw=fac00], ///
strata(estratoarea) vce(linearized) singleunit(certainty)
svy:regress log_money aproba1 if actpr2012==10
estimates store modelo1
Sampling weights: fac00
VCE: linearized
Single unit: certainty
Strata 1: estratoarea
Sampling unit 1: correlativo
FPC 1: <zero>
(running regress on estimation sample)
Survey: Linear regression
Number of strata = 119 Number of obs = 27,181
Number of PSUs = 1,663 Population size = 2,580,092
Design df = 1,544
F(1, 1544) = 2501.67
Prob > F = 0.0000
R-squared = 0.2018
------------------------------------------------------------------------------
| Linearized
log_money | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
aproba1 | .0698602 .0013967 50.02 0.000 .0671205 .0725999
_cons | 4.951058 .0133573 370.66 0.000 4.924858 4.977259
------------------------------------------------------------------------------
esttab modelo0 modelo1 (1) (2)
log_money log_money
--------------------------------------------
aproba1 0.0642*** 0.0699***
(74.07) (50.02)
_cons 4.973*** 4.951***
(606.25) (370.66)
--------------------------------------------
N 27181 27181
--------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001Predicciones
estimates restore modelo0
predict errores if _est_modelo0==1, res
predict y_hat if _est_modelo0==1, xb
(results modelo0 are active now)
(47,267 missing values generated)
(47,267 missing values generated)AnƔlisis de supuestos
Normalidad de los errores
histogram errores
sktest errores(bin=44, start=-4.4694438, width=.20683383)
Skewness and kurtosis tests for normality
----- Joint test -----
Variable | Obs Pr(skewness) Pr(kurtosis) Adj chi2(2) Prob>chi2
-------------+-----------------------------------------------------------------
errores | 27,181 0.0000 0.0000 . .Heterocedasticidad
scatter errores y_hat
scatter errores y_hat, jitter(20) mcolor(%20)
rvfplot
TambiĆ©n podemos hacer una prueba de hipĆ³tesis:
estat hettest
BreuschāPagan/CookāWeisberg test for heteroskedasticity
Assumption: Normal error terms
Variable: Fitted values of log_money
H0: Constant variance
chi2(1) = 100.97
Prob > chi2 = 0.0000Estas pruebas suponen independencia de las observaciones. Por lo cual no se puede aplicar algunas de estas pruebas para el diseƱo muestral complejo.
Datos atĆpicos
ĀæMejora el ajuste de nuestro modelo sin datos atĆpicos?
estat summarize Estimation sample regress Number of obs = 27,181
-------------------------------------------------------------------
Variable | Mean Std. dev. Min Max
-------------+-----------------------------------------------------
log_money | 5.49466 .7583819 1.098612 10.30962
aproba1 | 8.136603 4.844354 0 25
-------------------------------------------------------------------Pero si queremos ver la influencia de algunas observaciones:
predict residuos_est if _est_modelo0==1, rstandard
* Standardized residuals -- Valores de mƔs de3
(47,267 missing values generated)predict leverage if _est_modelo0==1, leverage
* Cuando leverage > 2k/n es "alta"
(47,267 missing values generated)estimates restore modelo0
dfbeta(results modelo0 are active now)
Generating DFBETA variable ...
(47,267 missing values generated)
_dfbeta_1: DFBETA aproba1predict cooksd if _est_modelo0==1, cooksd
*Valores mayores 4/N dan problema(47,267 missing values generated)regress log_money aproba1 if actpr2012==10 & residuos_est<3 Source | SS df MS Number of obs = 27,097
-------------+---------------------------------- F(1, 27095) = 5692.11
Model | 2612.16515 1 2612.16515 Prob > F = 0.0000
Residual | 12434.1703 27,095 .458910143 R-squared = 0.1736
-------------+---------------------------------- Adj R-squared = 0.1736
Total | 15046.3355 27,096 .555297294 Root MSE = .67743
------------------------------------------------------------------------------
log_money | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
aproba1 | .0641317 .00085 75.45 0.000 .0624656 .0657978
_cons | 4.964906 .0080477 616.93 0.000 4.949133 4.98068
------------------------------------------------------------------------------Es un mejor modelo Āæpero cĆ³mo justificarlo? Yo prefiero usar la regresiĆ³n robusta a datos atĆpicos. Porque podemos volver a hacer este proceso.
Modelo de regresiĆ³n lineal mĆŗltiple
IntroducciĆ³n de una variable categĆ³rica
Podemos crear una variable dummy o āficticiaā
tab r104, gen(s_)
regress log_money aproba1 s_2 if actpr2012==10
sexo | Freq. Percent Cum.
------------+-----------------------------------
hombre | 35,099 47.15 47.15
mujer | 39,349 52.85 100.00
------------+-----------------------------------
Total | 74,448 100.00
Source | SS df MS Number of obs = 27,181
-------------+---------------------------------- F(2, 27178) = 3405.84
Model | 3132.80256 2 1566.40128 Prob > F = 0.0000
Residual | 12499.5887 27,178 .459915693 R-squared = 0.2004
-------------+---------------------------------- Adj R-squared = 0.2003
Total | 15632.3913 27,180 .575143166 Root MSE = .67817
------------------------------------------------------------------------------
log_money | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
aproba1 | .0640287 .0008491 75.40 0.000 .0623644 .0656931
s_2 | -.2762078 .008318 -33.21 0.000 -.2925114 -.2599042
_cons | 5.091419 .0088009 578.51 0.000 5.074168 5.108669
------------------------------------------------------------------------------Esto es similar que usar la opciĆ³n āi.ā precedida de la que tenemos como variable dependiente. Ojo, la variable debe estar almacenada como double no como de cadena, para poder aplicar esta opciĆ³n.
regress log_money aproba1 i.r104 if actpr2012==10
estimates store modelo2 Source | SS df MS Number of obs = 27,181
-------------+---------------------------------- F(2, 27178) = 3405.84
Model | 3132.80256 2 1566.40128 Prob > F = 0.0000
Residual | 12499.5887 27,178 .459915693 R-squared = 0.2004
-------------+---------------------------------- Adj R-squared = 0.2003
Total | 15632.3913 27,180 .575143166 Root MSE = .67817
------------------------------------------------------------------------------
log_money | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
aproba1 | .0640287 .0008491 75.40 0.000 .0623644 .0656931
|
r104 |
mujer | -.2762078 .008318 -33.21 0.000 -.2925114 -.2599042
_cons | 5.091419 .0088009 578.51 0.000 5.074168 5.108669
------------------------------------------------------------------------------Si queremos cambiar la categorĆa de referencia:
regress log_money aproba1 ib1.r104 if actpr2012==10
Source | SS df MS Number of obs = 27,181
-------------+---------------------------------- F(2, 27178) = 3405.84
Model | 3132.80256 2 1566.40128 Prob > F = 0.0000
Residual | 12499.5887 27,178 .459915693 R-squared = 0.2004
-------------+---------------------------------- Adj R-squared = 0.2003
Total | 15632.3913 27,180 .575143166 Root MSE = .67817
------------------------------------------------------------------------------
log_money | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
aproba1 | .0640287 .0008491 75.40 0.000 .0623644 .0656931
|
r104 |
mujer | -.2762078 .008318 -33.21 0.000 -.2925114 -.2599042
_cons | 5.091419 .0088009 578.51 0.000 5.074168 5.108669
------------------------------------------------------------------------------Esta introducciĆ³n de las variables asume un cambio en el intercepto. Es necesario establecer cuĆ”nto se gana frente a la categorĆa de referencia. Manteniendo, los aƱos de escolaridad constantes.
esttab modelo0 modelo1 modelo2, ar2 (1) (2) (3)
log_money log_money log_money
------------------------------------------------------------
aproba1 0.0642*** 0.0699*** 0.0640***
(74.07) (50.02) (75.40)
1.r104 0
(.)
2.r104 -0.276***
(-33.21)
_cons 4.973*** 4.951*** 5.091***
(606.25) (370.66) (578.51)
------------------------------------------------------------
N 27181 27181 27181
adj. R-sq 0.168 0.200
------------------------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001Para poder usar variables categĆ³ricas de mejor manera, podemos utilizar este comando. Se parece a test, pero nos permite comparar modelos con āi.ā
ssc install ftestftest modelo0 modelo2Assumption: modelo0 nested in modelo2
F( 1, 27178) = 1102.65
prob > F = 0.0000Veamos quĆ© pasa con una variable de mĆ”s categorĆas
regress log_money aproba1 i.r104 i.region if actpr2012==10
estimates store modelo3 Source | SS df MS Number of obs = 27,181
-------------+---------------------------------- F(6, 27174) = 1200.35
Model | 3275.1224 6 545.853733 Prob > F = 0.0000
Residual | 12357.2689 27,174 .454746039 R-squared = 0.2095
-------------+---------------------------------- Adj R-squared = 0.2093
Total | 15632.3913 27,180 .575143166 Root MSE = .67435
-----------------------------------------------------------------------------------------------------
log_money | Coefficient Std. err. t P>|t| [95% conf. interval]
------------------------------------+----------------------------------------------------------------
aproba1 | .0610032 .0008622 70.76 0.000 .0593134 .0626931
|
r104 |
mujer | -.2799828 .0082747 -33.84 0.000 -.2962016 -.263764
|
region |
central i | .0287756 .0119746 2.40 0.016 .0053049 .0522464
central ii | -.0212401 .0133346 -1.59 0.111 -.0473766 .0048964
oriental | -.0294394 .0122659 -2.40 0.016 -.0534812 -.0053976
Ćrea metropolitana de san salvador | .188387 .013424 14.03 0.000 .1620753 .2146987
|
_cons | 5.089817 .011179 455.30 0.000 5.067905 5.111728
-----------------------------------------------------------------------------------------------------ĀæMejora nuestro modelo?
ftest modelo2 modelo3Assumption: modelo2 nested in modelo3
F( 4, 27174) = 78.24
prob > F = 0.0000IntroducciĆ³n de una variable numĆ©rica
Los coeficientes pueden leerse como derivadas parciales de una funciĆ³n lineal :)
regress log_money aproba1 i.r104 i.region r106 if actpr2012==10
estimates store modelo4 Source | SS df MS Number of obs = 27,181
-------------+---------------------------------- F(7, 27173) = 1231.28
Model | 3764.39125 7 537.770179 Prob > F = 0.0000
Residual | 11868 27,173 .436757075 R-squared = 0.2408
-------------+---------------------------------- Adj R-squared = 0.2406
Total | 15632.3913 27,180 .575143166 Root MSE = .66088
-----------------------------------------------------------------------------------------------------
log_money | Coefficient Std. err. t P>|t| [95% conf. interval]
------------------------------------+----------------------------------------------------------------
aproba1 | .0697546 .0008845 78.87 0.000 .068021 .0714882
|
r104 |
mujer | -.3017288 .0081353 -37.09 0.000 -.3176745 -.2857831
|
region |
central i | .0206726 .0117378 1.76 0.078 -.0023342 .0436794
central ii | -.0185689 .0130684 -1.42 0.155 -.0441837 .0070459
oriental | -.0308927 .0120209 -2.57 0.010 -.0544543 -.0073311
Ćrea metropolitana de san salvador | .1438722 .0132228 10.88 0.000 .1179547 .1697896
|
r106 | .009887 .0002954 33.47 0.000 .009308 .010466
_cons | 4.654994 .0169943 273.92 0.000 4.621684 4.688303
-----------------------------------------------------------------------------------------------------ĀæMejora nuestro modelo?
ftest modelo3 modelo4
Assumption: modelo3 nested in modelo4
F( 1, 27173) = 1120.23
prob > F = 0.0000Revisemos los modelos
esttab modelo*, ar2 label se (1) (2) (3) (4) (5)
log_money log_money log_money log_money log_money
----------------------------------------------------------------------------------------------------
nĆŗmero de grados a~s 0.0642*** 0.0699*** 0.0640*** 0.0610*** 0.0698***
(0.000866) (0.00140) (0.000849) (0.000862) (0.000884)
hombre 0 0 0
(.) (.) (.)
mujer -0.276*** -0.280*** -0.302***
(0.00832) (0.00827) (0.00814)
occidental 0 0
(.) (.)
central i 0.0288* 0.0207
(0.0120) (0.0117)
central ii -0.0212 -0.0186
(0.0133) (0.0131)
oriental -0.0294* -0.0309*
(0.0123) (0.0120)
Ćrea metropolitana~d 0.188*** 0.144***
(0.0134) (0.0132)
edad en aƱos cumpl~s 0.00989***
(0.000295)
Constant 4.973*** 4.951*** 5.091*** 5.090*** 4.655***
(0.00820) (0.0134) (0.00880) (0.0112) (0.0170)
----------------------------------------------------------------------------------------------------
Observations 27181 27181 27181 27181 27181
Adjusted R-squared 0.168 0.200 0.209 0.241
----------------------------------------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001AnƔlisis de supuestos
Para el caso de modelos con mĆŗltiples variables explicativas
Predicciones:
estimates restore modelo4
predict errores4 if _est_modelo4==1, res
predict y_hat4 if _est_modelo4==1, xb
(results modelo4 are active now)
(47,267 missing values generated)
(47,267 missing values generated)AnƔlisis de supuestos
Normalidad multivariada
mvtest normality log_money r106 aproba1 if actpr2012==10Test for multivariate normality
Doornik-Hansen chi2(6) = 5395.079 Prob>chi2 = 0.0000Normalidad de los errores
estimates restore modelo4
histogram errores4
sktest errores4(results modelo4 are active now)
(bin=44, start=-4.5629158, width=.20803703)
Skewness and kurtosis tests for normality
----- Joint test -----
Variable | Obs Pr(skewness) Pr(kurtosis) Adj chi2(2) Prob>chi2
-------------+-----------------------------------------------------------------
errores4 | 27,181 0.0000 0.0000 . .Heterocedasticidad
scatter errores y_hat4
scatter errores y_hat4, jitter(20) mcolor(%20)
rvfplot
TambiĆ©n podemos hacer una prueba de hipĆ³tesis:
estat hettest
BreuschāPagan/CookāWeisberg test for heteroskedasticity
Assumption: Normal error terms
Variable: Fitted values of log_money
H0: Constant variance
chi2(1) = 296.42
Prob > chi2 = 0.0000Stata ofrece varias formas de corregir la heterocedasticidad
regress log_money aproba1 i.r104 i.region r106 if actpr2012==10, robustLinear regression Number of obs = 27,181
F(7, 27173) = 1155.57
Prob > F = 0.0000
R-squared = 0.2408
Root MSE = .66088
-----------------------------------------------------------------------------------------------------
| Robust
log_money | Coefficient std. err. t P>|t| [95% conf. interval]
------------------------------------+----------------------------------------------------------------
aproba1 | .0697546 .0008996 77.54 0.000 .0679914 .0715178
|
r104 |
mujer | -.3017288 .008382 -36.00 0.000 -.318158 -.2852997
|
region |
central i | .0206726 .0115381 1.79 0.073 -.0019426 .0432878
central ii | -.0185689 .0130067 -1.43 0.153 -.0440627 .006925
oriental | -.0308927 .0125467 -2.46 0.014 -.0554848 -.0063006
Ćrea metropolitana de san salvador | .1438722 .012786 11.25 0.000 .1188111 .1689333
|
r106 | .009887 .0003248 30.44 0.000 .0092504 .0105237
_cons | 4.654994 .0172811 269.37 0.000 4.621122 4.688865
-----------------------------------------------------------------------------------------------------regress log_money aproba1 i.r104 i.region r106 if actpr2012==10, vce(hc2)Linear regression Number of obs = 27,181
F(7, 27173) = 1155.50
Prob > F = 0.0000
R-squared = 0.2408
Root MSE = .66088
-----------------------------------------------------------------------------------------------------
| Robust HC2
log_money | Coefficient std. err. t P>|t| [95% conf. interval]
------------------------------------+----------------------------------------------------------------
aproba1 | .0697546 .0008996 77.54 0.000 .0679914 .0715179
|
r104 |
mujer | -.3017288 .0083821 -36.00 0.000 -.3181581 -.2852995
|
region |
central i | .0206726 .011538 1.79 0.073 -.0019425 .0432877
central ii | -.0185689 .0130069 -1.43 0.153 -.0440631 .0069253
oriental | -.0308927 .0125466 -2.46 0.014 -.0554847 -.0063007
Ćrea metropolitana de san salvador | .1438722 .0127862 11.25 0.000 .1188107 .1689337
|
r106 | .009887 .0003248 30.44 0.000 .0092504 .0105237
_cons | 4.654994 .0172815 269.36 0.000 4.621121 4.688866
-----------------------------------------------------------------------------------------------------regress log_money aproba1 i.r104 i.region r106 if actpr2012==10, vce(hc3)Linear regression Number of obs = 27,181
F(7, 27173) = 1155.10
Prob > F = 0.0000
R-squared = 0.2408
Root MSE = .66088
-----------------------------------------------------------------------------------------------------
| Robust HC3
log_money | Coefficient std. err. t P>|t| [95% conf. interval]
------------------------------------+----------------------------------------------------------------
aproba1 | .0697546 .0008998 77.53 0.000 .067991 .0715182
|
r104 |
mujer | -.3017288 .0083833 -35.99 0.000 -.3181606 -.285297
|
region |
central i | .0206726 .0115396 1.79 0.073 -.0019456 .0432908
central ii | -.0185689 .013009 -1.43 0.153 -.0440672 .0069295
oriental | -.0308927 .0125484 -2.46 0.014 -.0554883 -.0062971
Ćrea metropolitana de san salvador | .1438722 .0127882 11.25 0.000 .1188066 .1689378
|
r106 | .009887 .0003249 30.43 0.000 .0092503 .0105238
_cons | 4.654994 .0172845 269.32 0.000 4.621115 4.688872
-----------------------------------------------------------------------------------------------------regress log_money aproba1 i.r104 i.region r106 if actpr2012==10, cluster(idboleta)Linear regression Number of obs = 27,181
F(7, 17017) = 1054.68
Prob > F = 0.0000
R-squared = 0.2408
Root MSE = .66088
(Std. err. adjusted for 17,018 clusters in idboleta)
-----------------------------------------------------------------------------------------------------
| Robust
log_money | Coefficient std. err. t P>|t| [95% conf. interval]
------------------------------------+----------------------------------------------------------------
aproba1 | .0697546 .000953 73.19 0.000 .0678865 .0716227
|
r104 |
mujer | -.3017288 .0082305 -36.66 0.000 -.3178615 -.2855961
|
region |
central i | .0206726 .0122783 1.68 0.092 -.0033942 .0447394
central ii | -.0185689 .0140144 -1.32 0.185 -.0460386 .0089008
oriental | -.0308927 .0135067 -2.29 0.022 -.0573672 -.0044181
Ćrea metropolitana de san salvador | .1438722 .0135948 10.58 0.000 .117225 .1705194
|
r106 | .009887 .0003312 29.85 0.000 .0092378 .0105363
_cons | 4.654994 .0179986 258.63 0.000 4.619714 4.690273
-----------------------------------------------------------------------------------------------------Multicolinealidad
estimate restore modelo4
vif
(results modelo4 are active now)
Variable | VIF 1/VIF
-------------+----------------------
aproba1 | 1.14 0.875308
2.r104 | 1.01 0.992737
region |
2 | 1.54 0.651111
3 | 1.41 0.709321
4 | 1.50 0.665922
5 | 1.48 0.674044
r106 | 1.11 0.903983
-------------+----------------------
Mean VIF | 1.31Post-estimaciĆ³n y cĆ”lculo de efecto marginales
Muchas veces para comunicar un modelo podemos valernos de predicciones o efectos marginales. Esto se realiza con el comando āmarginsā
Algunas formas de usar las predicciones:
margins r104Predictive margins Number of obs = 27,181
Model VCE: OLS
Expression: Linear prediction, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
r104 |
hombre | 5.623273 .0053003 1060.93 0.000 5.612884 5.633662
mujer | 5.321545 .0061527 864.92 0.000 5.309485 5.333604
------------------------------------------------------------------------------
margins r104##regionPredictive margins Number of obs = 27,181
Model VCE: OLS
Expression: Linear prediction, predict()
------------------------------------------------------------------------------------------------------------
| Delta-method
| Margin std. err. t P>|t| [95% conf. interval]
-------------------------------------------+----------------------------------------------------------------
r104 |
hombre | 5.623273 .0053003 1060.93 0.000 5.612884 5.633662
mujer | 5.321545 .0061527 864.92 0.000 5.309485 5.333604
|
region |
occidental | 5.475864 .0083099 658.96 0.000 5.459576 5.492152
central i | 5.496536 .0082909 662.96 0.000 5.480286 5.512787
central ii | 5.457295 .0101152 539.52 0.000 5.437469 5.477121
oriental | 5.444971 .0087264 623.97 0.000 5.427867 5.462075
Ćrea metropolitana de san salvador | 5.619736 .0101553 553.38 0.000 5.599831 5.639641
|
r104#region |
hombre#occidental | 5.604477 .0089586 625.60 0.000 5.586917 5.622036
hombre#central i | 5.625149 .0090017 624.90 0.000 5.607505 5.642793
hombre#central ii | 5.585908 .0106961 522.24 0.000 5.564943 5.606873
hombre#oriental | 5.573584 .0093779 594.33 0.000 5.555203 5.591965
hombre#Ćrea metropolitana de san salvador | 5.748349 .0107791 533.29 0.000 5.727221 5.769477
mujer#occidental | 5.302748 .0095889 553.01 0.000 5.283953 5.321543
mujer#central i | 5.323421 .0094956 560.62 0.000 5.304809 5.342033
mujer#central ii | 5.284179 .0111362 474.50 0.000 5.262351 5.306007
mujer#oriental | 5.271855 .0099119 531.87 0.000 5.252428 5.291283
mujer#Ćrea metropolitana de san salvador | 5.44662 .0111142 490.06 0.000 5.424836 5.468405
------------------------------------------------------------------------------------------------------------
margins sexo##regionvariable sexo not found
r(111);
end of do-file
r(111);TambiƩn hay otras opciones dydx(), eyex(), dyex(), eydx(). La mƔs usada es la primera
margins, dydx(*) variable sexo not found
r(111);
Average marginal effects Number of obs = 27,181
Model VCE: OLS
Expression: Linear prediction, predict()
dy/dx wrt: aproba1 2.r104 2.region 3.region 4.region 5.region r106
-----------------------------------------------------------------------------------------------------
| Delta-method
| dy/dx std. err. t P>|t| [95% conf. interval]
------------------------------------+----------------------------------------------------------------
aproba1 | .0697546 .0008845 78.87 0.000 .068021 .0714882
|
r104 |
mujer | -.3017288 .0081353 -37.09 0.000 -.3176745 -.2857831
|
region |
central i | .0206726 .0117378 1.76 0.078 -.0023342 .0436794
central ii | -.0185689 .0130684 -1.42 0.155 -.0441837 .0070459
oriental | -.0308927 .0120209 -2.57 0.010 -.0544543 -.0073311
Ćrea metropolitana de san salvador | .1438722 .0132228 10.88 0.000 .1179547 .1697896
|
r106 | .009887 .0002954 33.47 0.000 .009308 .010466
-----------------------------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.Estos comando serĆ”n aĆŗn mĆ”s importantes para la regresiĆ³n logĆstica.
CĆ³mo hacemos porque transformamos. Para esto podrĆamos usar la opciĆ³n de expresiĆ³n. Ojo que esto podrĆa ser interesante para presentar resultados, pero se tendrĆa que ajustar mejor la varianza. Checa esa opciĆ³n acĆ” https://www.stata.com/stata-news/news34-2/spotlight/
margins, expression(exp(predict(xb))*exp((`e(rmse)'^2)/2))
variable sexo not found
r(111);
Predictive margins Number of obs = 27,181
Model VCE: OLS
Expression: exp(predict(xb))*exp((.6608759909481651^2)/2)
------------------------------------------------------------------------------
| Delta-method
| Margin std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
_cons | 324.9672 1.395268 232.91 0.000 322.2326 327.7019
------------------------------------------------------------------------------Este es el valor dejando todos los valores constantes
Podemos incluir una variable:
margins r104, expression(exp(predict(xb))*exp((`e(rmse)'^2)/2))
mean money if _est_modelo4==1, over(r104) variable sexo not found
r(111);
Predictive margins Number of obs = 27,181
Model VCE: OLS
Expression: exp(predict(xb))*exp((.6608759909481651^2)/2)
------------------------------------------------------------------------------
| Delta-method
| Margin std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
r104 |
hombre | 366.2156 2.023701 180.96 0.000 362.2492 370.182
mujer | 270.8306 1.701886 159.14 0.000 267.495 274.1662
------------------------------------------------------------------------------
Mean estimation Number of obs = 27,181
--------------------------------------------------------------
| Mean Std. err. [95% conf. interval]
-------------+------------------------------------------------
c.money@r104 |
hombre | 347.6122 3.433204 340.883 354.3415
mujer | 286.051 2.699843 280.7592 291.3428
--------------------------------------------------------------PresentaciĆ³n de resultados
Tablas de coeficientes y estimaciones
Como ya observamos, las tablas con esttab son muy fĆ”ciles. Podemos comparar nuestros resultados. Hemos ido utilizando estas tablas, podemos usar la opciĆ³n āstatsā para ir modificando quĆ© escalares del modelo queremos.
estimates restore modelo4
ereturn list
variable sexo not found
r(111);
(results modelo4 are active now)
scalars:
e(rank) = 8
e(ll_0) = -31050.26959045027
e(ll) = -27306.09470708167
e(r2_a) = .2406115538050895
e(rss) = 11868.00001016265
e(mss) = 3764.391250427603
e(rmse) = .6608759909481651
e(r2) = .2408071284601065
e(F) = 1231.279832445927
e(df_r) = 27173
e(df_m) = 7
e(N) = 27181
macros:
e(cmdline) : "regress log_money aproba1 i.r104 i.region r106 if actpr2012==10"
e(title) : "Linear regression"
e(marginsok) : "XB default"
e(vce) : "ols"
e(depvar) : "log_money"
e(cmd) : "regress"
e(properties) : "b V"
e(predict) : "regres_p"
e(model) : "ols"
e(estat_cmd) : "regress_estat"
matrices:
e(b) : 1 x 10
e(V) : 10 x 10
functions:
e(sample) Con ello podemos elegir los nombres de nuestros escalares para incluir en el modelo
esttab modelo0 modelo2 modelo3 modelo4, label stats(N r2_a F) se variable sexo not found
r(111);
------------------------------------------------------------------------------------
(1) (2) (3) (4)
log_money log_money log_money log_money
------------------------------------------------------------------------------------
nĆŗmero de grados a~s 0.0642*** 0.0640*** 0.0610*** 0.0698***
(0.000866) (0.000849) (0.000862) (0.000884)
hombre 0 0 0
(.) (.) (.)
mujer -0.276*** -0.280*** -0.302***
(0.00832) (0.00827) (0.00814)
occidental 0 0
(.) (.)
central i 0.0288* 0.0207
(0.0120) (0.0117)
central ii -0.0212 -0.0186
(0.0133) (0.0131)
oriental -0.0294* -0.0309*
(0.0123) (0.0120)
Ćrea metropolitana~d 0.188*** 0.144***
(0.0134) (0.0132)
edad en aƱos cumpl~s 0.00989***
(0.000295)
Constant 4.973*** 5.091*** 5.090*** 4.655***
(0.00820) (0.00880) (0.0112) (0.0170)
------------------------------------------------------------------------------------
N 27181 27181 27181 27181
r2_a 0.168 0.200 0.209 0.241
F 5486.6 3405.8 1200.3 1231.3
------------------------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001TambiƩn podemos exportar nuestros resultados
esttab modelo0 modelo2 modelo3 modelo4 using "out/resultados.rtf", label stats(N r2_a F) se
esttab modelo0 modelo2 modelo3 modelo4 using "out/resultados.csv", label stats(N r2_a F) se
variable sexo not found
r(111);
file out/resultados.rtf already exists
r(602);
end of do-file
r(602);Para mĆ”s inspiraciĆ³n de tablas http://repec.org/bocode/e/estout/esttab.html
GraficaciĆ³n de coeficientes y efectos marginales
Podemos utilizar:
ssc install coefplot, replace
coefplot modelo0 modelo2 modelo3 modelo4, drop(_cons) title("Resultados de los modelos") xline(0) variable sexo not found
r(111);
TIP: TambiƩn se pueden guardar estimaciones hecha con margin y se pueden graficar
estimates restore modelo4
margins, at(r106=(20(5)50)) expression(exp(predict(xb))*exp((`e(rmse)'^2)/2))
marginsplot, title("PredicciĆ³n de los ingresos") ylabel("DĆ³lares mensuales")
variable sexo not found
r(111);
(results modelo4 are active now)
Predictive margins Number of obs = 27,181
Model VCE: OLS
Expression: exp(predict(xb))*exp((.6608759909481651^2)/2)
1._at: r106 = 20
2._at: r106 = 25
3._at: r106 = 30
4._at: r106 = 35
5._at: r106 = 40
6._at: r106 = 45
7._at: r106 = 50
------------------------------------------------------------------------------
| Delta-method
| Margin std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
_at |
1 | 270.8593 1.800919 150.40 0.000 267.3296 274.3891
2 | 284.5858 1.593738 178.57 0.000 281.4621 287.7095
3 | 299.0079 1.430234 209.06 0.000 296.2047 301.8111
4 | 314.1609 1.360723 230.88 0.000 311.4939 316.8278
5 | 330.0818 1.438933 229.39 0.000 327.2615 332.902
6 | 346.8095 1.685164 205.80 0.000 343.5066 350.1123
7 | 364.3849 2.079873 175.20 0.000 360.3084 368.4614
------------------------------------------------------------------------------
Variables that uniquely identify margins: r106
invalid label specifier, : "DĆ³lares mensuales":
r(198);
end of do-file
r(198);